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Volume 28, Issue 3
Random Attractor for the Nonclassical Diffusion Equation with Fading Memory

Shuilin Cheng

DOI: 10.4208/jpde.v28.n3.4

J. Part. Diff. Eq., 28 (2015), pp. 253-268.

Published online: 2015-09

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  • Abstract
In this paper,we consider the stochastic nonclassical diffusion equationwith fading memory on a bounded domain. By decomposition of the solution operator, we give the necessary condition of asymptotic smoothness of the solution to the initial boundary value problem, and then we prove the existence of a random attractor in the space $M_1=D(A^{\frac{1}{2}}) × L^2_μ(R^+, D(A^{\frac{1}{2}}))$, where A=-Δ with Dirichlet boundary condition.
  • Keywords

Stochastic nonclassical diffusion equations fading memory random attractor

  • AMS Subject Headings

35B40, 35B41, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

chengslzncd@znufe.edu.cn (Shuilin Cheng)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-28-253, author = {Cheng , Shuilin}, title = {Random Attractor for the Nonclassical Diffusion Equation with Fading Memory}, journal = {Journal of Partial Differential Equations}, year = {2015}, volume = {28}, number = {3}, pages = {253--268}, abstract = { In this paper,we consider the stochastic nonclassical diffusion equationwith fading memory on a bounded domain. By decomposition of the solution operator, we give the necessary condition of asymptotic smoothness of the solution to the initial boundary value problem, and then we prove the existence of a random attractor in the space $M_1=D(A^{\frac{1}{2}}) × L^2_μ(R^+, D(A^{\frac{1}{2}}))$, where A=-Δ with Dirichlet boundary condition.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v28.n3.4}, url = {http://global-sci.org/intro/article_detail/jpde/5113.html} }
TY - JOUR T1 - Random Attractor for the Nonclassical Diffusion Equation with Fading Memory AU - Cheng , Shuilin JO - Journal of Partial Differential Equations VL - 3 SP - 253 EP - 268 PY - 2015 DA - 2015/09 SN - 28 DO - http://doi.org/10.4208/jpde.v28.n3.4 UR - https://global-sci.org/intro/article_detail/jpde/5113.html KW - Stochastic nonclassical diffusion equations KW - fading memory KW - random attractor AB - In this paper,we consider the stochastic nonclassical diffusion equationwith fading memory on a bounded domain. By decomposition of the solution operator, we give the necessary condition of asymptotic smoothness of the solution to the initial boundary value problem, and then we prove the existence of a random attractor in the space $M_1=D(A^{\frac{1}{2}}) × L^2_μ(R^+, D(A^{\frac{1}{2}}))$, where A=-Δ with Dirichlet boundary condition.
Cheng , Shuilin. (2015). Random Attractor for the Nonclassical Diffusion Equation with Fading Memory. Journal of Partial Differential Equations. 28 (3). 253-268. doi:10.4208/jpde.v28.n3.4
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